1 Area of Interest (AOI)

Our area of interest is located in the southern part of the state of Salzburg close to Schmitten and Viehhofen cities. It is a small catchment of 120 km2 draining to the Saalach river. The elevation data for this assignment was obtained from the product ALOS World 3D (AW3D30). In the map below, we display the slope and the stream network and basin delineation according to the official information of the Land Salzburg.

Mouse over the pixels to obtain the slope value.

2 Slope distribution

Considering the slope classification of V. Zhuchkova and E. Rakovskaya, 2017. On average, this catchment could be classified as very steep, presenting the lowest values near to the main river and the highest ones close to the drainage divide.

3 How to estimate the curvature? - I

In simple words, we can define the curvature as the second derivative of a surface, or the slope of the slope. In surface water hydrology, the concept of curvature plays an important role to understand where the water drains off.

A negative value indicates that the surface is upwardly convex at that cell, and flow will be decelerated. A positive profile indicates that the surface is upwardly concave at that cell, and the flow will be accelerated. A value of zero indicates that the surface is linear (See curvature function ArcGIS). The map below displays the profile curvature for our study area.

Mouse over the pixels to obtain the profile curvature values.

4 How to estimate the curvature? - II

However, the curvature is not the only model that explains deformations. Other models like the TPI (Topographic Position Index) given also information about the convex or concave of the terrain. In a TPI model the negative values, represent valleys, canyon, and bottoms, and the positive values ridges and hilltops. To estimate the TPI we need to apply a convolution operator and estimate the difference between the value of a cell and the mean value of its 8 surrounding cells.

Mouse over the pixels to obtain the TPI values.

5 Slope according to the altitute

For analyzing the local behavior of the slope. The entire catchment was divided into smaller units according to 200m elevation stripes.

The results show that the slope values are linearly correlated with the elevation until the 1500 m.a.s.l.

6 Cellsize importance

This example shows how different is the spatial distribution of slope values if it is used a digital elevation model of 120 m instead of 30 m of spatial resolution.

As it can notice, a larger cell size generates values closer to the mean.

7 Conclusion

Terrain analysis is the basis of several earth observation projects. The digital terrain models (DTM) derived from DEM, show us that in this specific catchment:

  • The slope change according to the altitude until the 1500 m.a.s.l.

  • There is more common to find negative curvature values in the valleys (low altitude areas).

  • And finally, the cell size (from 30 to 120 meters) changes sightly the first and second statistical moments of the distribution of slope values.